Non-uniform magnetic fields for collective behavior of self-assembled magnetic pillars

Programmable and self-assembled magnetic pillars are essential to expanding the application domain of magnetic microparticle collectives. Typically, the collective behavior of self-assembled magnetic pillars is carried out by generating uniform and time-varying magnetic fields. However, magnetic field-shaping capabilities employing non-uniform fields have not been explored for magnetic pillars. In this study, we generate non-uniform magnetic fields using a nine-coil electromagnetic system to achieve object manipulation, upstream/downstream locomotion, and independent actuation. We begin analyzing the static magnetic self-assembly of reduced iron microparticles and experimentally derive the average dimensions (height and diameter) of the resulting pillars. Subsequently, we delve into the collective dynamic response under non-uniform and time-varying magnetic fields, unveiling four distinct modalities. In order to demonstrate the versatility of our approach, we extend our study to the two-dimensional manipulation of a millimeter-sized glass bead using a precessing magnetic field describing a Lissajous curve. Moreover, we showcase the ability of magnetic pillars to adapt to confined and dynamic conditions within fluidic tubes. We finally present a noteworthy case where the nine-coil electromagnetic system independently actuates two clusters of magnetic pillars. Our study shows the potential of using non-uniform magnetic fields to actuate self-assembled magnetic pillars, enabling morphology reconfiguration capabilities, object manipulation, locomotion, and independent actuation.